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Crime, Punishment, and Evolution in an Adversarial Game


  • Michael McBride

    () (Department of Economics, University of California-Irvine)

  • Ryan Kendall

    () (Department of Economics, University of California-Irvine)

  • Martin B. Short

    () (Department of Mathematics, University of California-Los Angeles)

  • Maria R. D'Orsogna

    () (Department of Mathematics, California State University-Northridge)


We examine the game theoretic properties of a model of crime first introduced by Short, Brantingham, and D'Orsogna (Short et al. 2010) as the SBD Adversarial Game. We identify the rationalizable strategies and one-shot equilibria under mul- tiple equilibrium refinements. We further show that SBD's main result about the effectiveness of defecting-punishers in driving the system to evolve to the cooperative equilibrium under an imitation dynamic does generalize to a best response dynamic, although the nature of this strategy's role differs significantly between the two dynamics. The analysis reveals that the positive externality in punishing crime in the SBD game converts the adversarial setting from a social dilemma to a coordination game. We provide policy implications and lessons learned about the evolution of cooperation more generally.

Suggested Citation

  • Michael McBride & Ryan Kendall & Martin B. Short & Maria R. D'Orsogna, 2012. "Crime, Punishment, and Evolution in an Adversarial Game," Working Papers 121308, University of California-Irvine, Department of Economics.
  • Handle: RePEc:irv:wpaper:121308

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    References listed on IDEAS

    1. Fender, John, 1999. "A general equilibrium model of crime and punishment," Journal of Economic Behavior & Organization, Elsevier, vol. 39(4), pages 437-453, July.
    2. Fudenberg, Drew & Pathak, Parag A., 2010. "Unobserved punishment supports cooperation," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 78-86, February.
    3. Cinyabuguma, Matthias & Page, Talbot & Putterman, Louis, 2005. "Cooperation under the threat of expulsion in a public goods experiment," Journal of Public Economics, Elsevier, vol. 89(8), pages 1421-1435, August.
    4. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
    5. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    6. Eaton, B.Curtis & Wen, Jean-Fran├žois, 2008. "Myopic deterrence policies and the instability of equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 609-624, March.
    7. Ananish Chaudhuri, 2011. "Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature," Experimental Economics, Springer;Economic Science Association, vol. 14(1), pages 47-83, March.
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    More about this item


    Cooperation; Punishment; Evolution;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions


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